Support for TPTP's TFF0 (with arithmetic)

This commit reverses an "SZS ontology compliance hack" that was
done for CASC-24 this year, and adds a TPTP pretty-printer which
is capable of outputting results in the TPTP way (rather than the
SMT way).

This commit includes minor changes to the Expr package to add
obvious missing functionality, and to fix the way expressions
with builtin operators are made.  These changes are truly a
_fix_, the implementation had not been properly aligned with
the design vision for some corner cases.

1 files changed, 309 insertions, 0 deletions

diff --git a/test/regress/regress0/tptp/SYN000=2.p b/test/regress/regress0/tptp/SYN000=2.p
new file mode 100644
index 000000000..802613f4b
--- /dev/null
+++ b/test/regress/regress0/tptp/SYN000=2.p
@@ -0,0 +1,309 @@
+%------------------------------------------------------------------------------
+% File     : SYN000=2 : TPTP v5.5.0. Bugfixed v5.5.1.
+% Domain   : Syntactic
+% Problem  : TF0 syntax with arithmetic
+% Version  : Biased.
+% English  : 
+
+% Refs     :
+% Source   : [TPTP]
+% Names    :
+
+% Status   : Theorem
+% Rating   : ? v5.5.1
+% Syntax   : Number of formulae    :   83 (  73 unit;   6 type)
+%            Number of atoms       :  100 (   4 equality)
+%            Maximal formula depth :    7 (   1 average)
+%            Number of connectives :   14 (   0   ~;  10   |;   1   &)
+%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
+%            Number of predicates  :   20 (  10 propositional; 0-2 arity)
+%            Number of functors    :   41 (  24 constant; 0-2 arity)
+%            Number of variables   :   14 (   1 sgn;   3   !;  11   ?)
+%            Maximal term depth    :    3 (   1 average)
+%            Arithmetic symbols    :   37 (   9 pred;    7 func;   21 numbers)
+% SPC      : TF0_THM_EQU_ARI
+
+% Comments : 
+% Bugfixes : v5.5.1 - Removed $evaleq.
+%------------------------------------------------------------------------------
+%----Types for what follows
+tff(p_int_type,type,(
+    p_int: $int > $o )).
+
+tff(p_rat_type,type,(
+    p_rat: $rat > $o )).
+
+tff(p_real_type,type,(
+    p_real: $real > $o )).
+
+tff(a_int,type,(
+    a_int: $int )).
+
+tff(a_rat,type,(
+    a_rat: $rat )).
+
+tff(a_real,type,(
+    a_real: $real )).
+
+%----Numbers
+tff(integers,axiom,
+    ( p_int(123)
+    | p_int(-123) )).
+
+tff(rationals,axiom,
+    ( p_rat(123/456)
+    | p_rat(-123/456)
+    | p_rat(123/456) )).
+
+tff(reals,axiom,
+    ( p_real(123.456)
+    | p_real(-123.456)
+    | p_real(123.456E78)
+    | p_real(123.456e78)
+    | p_real(-123.456E78)
+    | p_real(123.456E-78)
+    | p_real(-123.456E-78) )).
+
+%----Variables
+tff(variables_int,axiom,(
+    ! [X: $int] :
+    ? [Y: $int] :
+      ( p_int(X)
+     => p_int(Y) ) )).
+
+tff(variables_rat,axiom,(
+    ! [X: $rat] :
+    ? [Y: $rat] :
+      ( p_rat(X)
+     => p_rat(Y) ) )).
+
+tff(variables_real,axiom,(
+    ! [X: $real] :
+    ? [Y: $real] :
+      ( p_real(X)
+     => p_real(Y) ) )).
+
+%----Arithmetic relations
+tff(less_int,axiom,(
+    $less(a_int,3) )).
+
+tff(less_rat,axiom,(
+    $less(a_rat,3/9) )).
+
+tff(less_real,axiom,(
+    $less(a_real,3.3) )).
+
+tff(lesseq_int,axiom,(
+    $lesseq(a_int,3) )).
+
+tff(lesseq_rat,axiom,(
+    $lesseq(a_rat,3/9) )).
+
+tff(lesseq_real,axiom,(
+    $lesseq(a_real,3.3) )).
+
+tff(greater_int,axiom,(
+    $greater(a_int,-3) )).
+
+tff(greater_rat,axiom,(
+    $greater(a_rat,-3/9) )).
+
+tff(greater_real,axiom,(
+    $greater(a_real,-3.3) )).
+
+tff(greatereq_int,axiom,(
+    $greatereq(a_int,-3) )).
+
+tff(greatereq_rat,axiom,(
+    $greatereq(a_rat,-3/9) )).
+
+tff(greatereq_real,axiom,(
+    $greatereq(a_real,-3.3) )).
+
+tff(equal_int,axiom,(
+    a_int = 0 )).
+
+tff(equal_rat,axiom,(
+    a_rat = 0/1 )).
+
+tff(equal_real,axiom,(
+    a_real = 0.0 )).
+
+%----Arithmetic functions
+tff(uminus_int,axiom,(
+    p_int($uminus(3)) )).
+
+tff(uminus_rat,axiom,(
+    p_rat($uminus(3/9)) )).
+
+tff(uminus_real,axiom,(
+    p_real($uminus(3.3)) )).
+
+tff(sum_int,axiom,(
+    p_int($sum(3,3)) )).
+
+tff(sum_rat,axiom,(
+    p_rat($sum(3/9,3/9)) )).
+
+tff(sum_real,axiom,(
+    p_real($sum(3.3,3.3)) )).
+
+tff(difference_int,axiom,(
+    p_int($difference(3,3)) )).
+
+tff(difference_rat,axiom,(
+    p_rat($difference(3/9,3/9)) )).
+
+tff(difference_real,axiom,(
+    p_real($difference(3.3,3.3)) )).
+
+tff(product_int,axiom,(
+    p_int($product(3,3)) )).
+
+tff(product_rat,axiom,(
+    p_rat($product(3/9,3/9)) )).
+
+tff(product_real,axiom,(
+    p_real($product(3.3,3.3)) )).
+
+tff(quotient_rat,axiom,(
+    p_rat($quotient(3/9,3/9)) )).
+
+tff(quotient_real,axiom,(
+    p_real($quotient(3.3,3.3)) )).
+
+tff(quotient_e_int,axiom,(
+    p_int($quotient_e(3,3)) )).
+
+tff(quotient_e_rat,axiom,(
+    p_rat($quotient_e(3/9,3/9)) )).
+
+tff(quotient_e_real,axiom,(
+    p_real($quotient_e(3.3,3.3)) )).
+
+tff(quotient_t_int,axiom,(
+    p_int($quotient_t(3,3)) )).
+
+tff(quotient_t_rat,axiom,(
+    p_rat($quotient_t(3/9,3/9)) )).
+
+tff(quotient_t_real,axiom,(
+    p_real($quotient_t(3.3,3.3)) )).
+
+tff(quotient_f_int,axiom,(
+    p_int($quotient_f(3,3)) )).
+
+tff(quotient_f_rat,axiom,(
+    p_rat($quotient_f(3/9,3/9)) )).
+
+tff(quotient_f_real,axiom,(
+    p_real($quotient_f(3.3,3.3)) )).
+
+tff(remainder_e_int,axiom,(
+    p_int($remainder_e(3,3)) )).
+
+tff(remainder_e_rat,axiom,(
+    p_rat($remainder_e(3/9,3/9)) )).
+
+tff(remainder_e_real,axiom,(
+    p_real($remainder_e(3.3,3.3)) )).
+
+tff(remainder_t_int,axiom,(
+    p_int($remainder_t(3,3)) )).
+
+tff(remainder_t_rat,axiom,(
+    p_rat($remainder_t(3/9,3/9)) )).
+
+tff(remainder_t_real,axiom,(
+    p_real($remainder_t(3.3,3.3)) )).
+
+tff(remainder_f_int,axiom,(
+    p_int($remainder_f(3,3)) )).
+
+tff(remainder_f_rat,axiom,(
+    p_rat($remainder_f(3/9,3/9)) )).
+
+tff(remainder_f_real,axiom,(
+    p_real($remainder_f(3.3,3.3)) )).
+
+tff(floor_int,axiom,(
+    p_int($floor(3)) )).
+
+tff(floor_rat,axiom,(
+    p_rat($floor(3/9)) )).
+
+tff(floor_int,axiom,(
+    p_real($floor(3.3)) )).
+
+tff(ceiling_int,axiom,(
+    p_int($ceiling(3)) )).
+
+tff(ceiling_rat,axiom,(
+    p_rat($ceiling(3/9)) )).
+
+tff(ceiling_int,axiom,(
+    p_real($ceiling(3.3)) )).
+
+tff(truncate_int,axiom,(
+    p_int($truncate(3)) )).
+
+tff(truncate_rat,axiom,(
+    p_rat($truncate(3/9)) )).
+
+tff(truncate_int,axiom,(
+    p_real($truncate(3.3)) )).
+
+%----Recognizing numbers
+tff(is_int_int,axiom,(
+    ? [X: $int] : $is_int(X) )).
+
+tff(is_int_rat,axiom,(
+    ? [X: $rat] : $is_int(X) )).
+
+tff(is_int_real,axiom,(
+    ? [X: $real] : $is_int(X) )).
+
+tff(is_rat_rat,axiom,(
+    ? [X: $rat] : $is_rat(X) )).
+
+tff(is_rat_real,axiom,(
+    ? [X: $real] : $is_rat(X) )).
+
+%----Coercion
+tff(to_int_int,axiom,(
+    p_int($to_int(3)) )).
+
+tff(to_int_rat,axiom,(
+    p_int($to_int(3/9)) )).
+
+tff(to_int_real,axiom,(
+    p_int($to_int(3.3)) )).
+
+tff(to_rat_int,axiom,(
+    p_rat($to_rat(3)) )).
+
+tff(to_rat_rat,axiom,(
+    p_rat($to_rat(3/9)) )).
+
+tff(to_rat_real,axiom,(
+    p_rat($to_rat(3.3)) )).
+
+tff(to_real_int,axiom,(
+    p_real($to_real(3)) )).
+
+tff(to_real_rat,axiom,(
+    p_real($to_real(3/9)) )).
+
+tff(to_real_real,axiom,(
+    p_real($to_real(3.3)) )).
+
+%----A conjecture to prove
+tff(mixed,conjecture,(
+    ? [X: $int,Y: $rat,Z: $real] :
+      ( Y = $to_rat($sum(X,2))
+      & ( $less($to_int(Y),3)
+        | $greater($to_real(Y),3.3) ) ) )).
+
+%------------------------------------------------------------------------------